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<p><dfn class="terminology">Theorem</dfn> If (<a href="" class="xref" data-knowl="./knowl/eq7_6.html" title="Equation 6.1.6">(6.1.6)</a>) is the general solution of the homogeneous equation and <span class="process-math">\({\bf x}^{(p)}\)</span> is a particular solution of the inhomogeneous equation (<a href="" class="xref" data-knowl="./knowl/eq7_4.html" title="Equation 6.1.4">(6.1.4)</a>), the general solution for (<a href="" class="xref" data-knowl="./knowl/eq7_4.html" title="Equation 6.1.4">(6.1.4)</a>) is given by</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq7_6.html ./knowl/eq7_4.html ./knowl/eq7_4.html">
\begin{equation*}
{\bf x}=C_1 {\bf x}^{(1)}+C_2 {\bf x}^{(2)}+\cdots C_n {\bf x}^{(n)}+{\bf x}^{(p)}
\end{equation*}
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